if we admit both senses, to the degree that nature is not 'well-regulated' in the 2nd sense ('efficient'), it is because it is not well-regulated in the 1st sense ('extension'). There's a logical priority here which one must be careful to attend to. — StreetlightX
I'm still thinking about the negativity of what we can call natural laws. — Akanthinos
The usual view is that physics must find something definite, crisp, determinate, atomistic, once it drills down to the bedrock of existence. This is why the micro-physical laws are taken to describe something substantially real while the macro-physical laws - like the second law of thermodynamics in particular - are dismissed as merely emergent in the sense of being descriptive illusions. A way of summing over the fine detail as a convenience. — apokrisis
This is why the micro-physical laws are taken to describe something substantially real while the macro-physical laws - like the second law of thermodynamics in particular - are dismissed as merely emergent in the sense of being descriptive illusions. A way of summing over the fine detail as a convenience. — apokrisis
Rosen's modelling relations constitute a conceptual schema for the understanding of the bidirectional process of correspondence between natural systems and formal symbolic systems. The notion of formal systems used in this study refers to information structures constructed as algebraic rings of observable attributes of natural systems, in which the notion of observable signifies a physical attribute that, in principle, can be measured. Due to the fact that modelling relations are bidirectional by construction, they admit a precise categorical formulation in terms of the category-theoretic syntactic language of adjoint functors, representing the inverse processes of information encoding/decoding via adjunctions. As an application, we construct a topological modelling schema of complex systems. The crucial distinguishing requirement between simple and complex systems in this schema is reflected with respect to their rings of observables by the property of global commutativity. The global information structure representing the behaviour of a complex system is modelled functorially in terms of its spectrum functor. An exact modelling relation is obtained by means of a complex encoding/decoding adjunction restricted to an equivalence between the category of complex information structures and the category of sheaves over a base category of partial or local information carriers equipped with an appropriate topology.
I'm tempted to try to start a reading group for this paper discussing Rosen: — fdrake
Due to the fact that modelling relations are bidirectional by construction, they admit a precise categorical formulation in terms of the category-theoretic syntactic language of adjoint functors, representing the inverse processes of information encoding/decoding via adjunctions.
I was thinking about this too, and especially the curious idea - let me know if you agree - that even positive injunctions in the law are, in a way, simply double negatives. — StreetlightX
There are no special constitutional Laws of Nature, or perhaps, the things we call Laws of Nature can only be so by analogy to constitutional law. — Akanthinos
The deepest physical laws look to capture mathematical symmetries. This is in fact a theorem - Noether's theorem. — apokrisis
If you don't want to mention the word "law" for some reason - and remember it's not me that defends the term - then what exactly would you like to call this kind of universal if-then statement? — apokrisis
In practice engineers handle irreversible processes with old fashioned phenomenological laws describing the flow (or flux) of the quantity under study. Most of these laws have been known for quite a long time. For example there is Fick's law... Equally simple laws describe other processes: Fourier's law for heat flow, Newton's law for sheering force (momentum flux) and Ohm's law for electric current....
The trouble is that each equation is a ceteris paribus law. It describes the flux only so long as just one kind of cause is operating. [Vector addition] if it works, buys facticity, but it is of little benefit to (law) realists who believe that the phenomena of nature flow from a small number of abstract, fundamental laws. — StreetlightX
Today, we use the Lagrangian method to describe all of physics, not just mechanics. All fundamental laws of physics can be expressed in terms of a least action principle. This is true for electromagnetism, special and general relativity, particle physics, and even more speculative pursuits that go beyond known laws of physics such as string theory.
http://www.damtp.cam.ac.uk/user/db275/concepts/LeastAction.pdf
I don't see a whole lot of conflict between your (1) and (3) (leaving God out of the picture.) — Wayfarer
Global regularities that 'emerge' could easily be simply another way of saying 'laws of nature'. — Wayfarer
And my view is that whilst the laws or principles of nature that science discovers provide explanations across whole swathes of the phenomenal domain, science doesn't necessarily explain those principles. I suppose I have an instrumentalist or pragmatic view - that science is useful and powerful, but it's not inherently meaningful in an existential sense. — Wayfarer
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.